Nick certainly didnt mind Combustion Man and Zhao having very clear deaths, the implied sex between Sokka and Suki or the genocide of an entire race; the issue with Jet was that it was a grown man killing a teenager.

Actually, it may have been a teen killing a teen. As Longshot moved towards Jet, he drew his bow. Watching it the first time, I figured, hey, maybe he's getting ready to fight, although the facility was pretty much empty. However, having them show the murder suicide, and looking back, I'm thinking there may have been some darker implications in Longshot's gesture.

tl;dr, the way they played out the scene, Longshot may have actually put Jet out of his misery, instead of letting him linger in pain.